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Simply put det(A)=0 and check for that value of c if det(A:B)!=0 then system is inconsistent as both rank(A) and rank(A:B) will be different then.

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(Solved now) Gateoverflow test doubt
In this question – https://gateoverflow.in/348646/Gate-overflow-linear-algebra-1-10 for $A=\begin{bmatrix} 0 & i\\ -i& 0 \end{bmatrix}$ how is (B) valid ?
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